A large number of gradient-based MRI techniques have been developed since its independent invention by Paul Lauterbur and Peter Mansfield in 1973, following the invention of the static technique of Damadian in 1972. Most modern MRI systems utilize a superconducting solenoid to establish a uniform B.sub.0 (or B.sub.Z) over the imaging volume. This results in the magnetic field being colinear with the path available for sample access. Coils are then required to produce monotonic (preferably linear) gradients in B.sub.Z with respect to x, y, and z over the sample region during precisely determined pulse sequences. The transverse gradients (.delta.B.sub.Z /.delta.x, .delta.B.sub.Z /.delta.y) in the prior art have generally been established by symmetrically located sets of saddle coils, similar to those first described by Golay in U.S. Pat. No. 3,569,823 or by related planar coils as disclosed by Roemer, U.S. Pat. No. 4,926,125 and Morich et al., U.S. Pat. No. 5,036,282. Maxwell pairs are universally used to generate the axial gradient, notwithstanding the incorrect usage of the word "toroidal" by Frese and Siebold in U.S. Pat. No. 4,468,622. The instant invention achieves order-of-magnitude improvements in several critical parameters for transverse gradient coils: acoustic noise, DC gradient efficiency, and high-speed switching efficiency.
The closest prior art to the instant invention, in terms of magnetic field configuration, appears to be the trapezium loops for use with an electromagnet, as disclosed in the article "Magnetic Field Gradient Coils for NMR Imaging" by Bangert and Mansfield in Journal Physics, E, 15, 235 (1982). The semi-cylindrical concept depicted by Mansfield in U.S. Pat. No. 4,165,479, while having some similar features, is not closely related, as its major field component is orthogonal to B.sub.Z.
The gradient pulses induce eddy currents and vibrations in nearby conducting structures (especially in flimsy shields, in the cryostat, and in light-weight rf coils) which perturb the field homogeneity following the pulses with time and spatial dependencies that are not easily characterized. Active shielding coils, were first publicly disclosed by Mansfield in 2/1986 at approximately the same time that Roemer filed the patent application which resulted in U.S. Pat. No. 4,737,716. Prior independent work was underway at Doty Scientific, who shipped the first such commercially available coils in 1/1987. FIG. 1 approximately depicts typical shielded Golay coils to generate .delta.B.sub.Z /.delta.x in the sample in the vicinity of the origin. A similar set of concentric coils, rotated 90.degree., is used to generate .delta.B.sub.Z /.delta.y. FIG. 2 shows second-order shielding of the Maxwell pair, or anti-Helmholtz coils, as used to generate linear .delta.B.sub.Z /.delta.z near the origin. Gradient coils 201, 202 at mean location z.apprxeq..+-.r.sub.f have about 2.5 times the amp-turns of shield coils 203, 204 when s.apprxeq.0.3 r.sub.f. Axial shield coils 205, 206 have about one-tenth the amp-turns of the gradient coils. Gradient linearity of .+-.20% is achieved over a sphere of radius 0.7 r.sub.f, and leakage flux through a cylinder of radius 1.4 r.sub.f is reduced by a order of magnitude compared to the unshielded case. Higher-order shielding achieves another order-of-magnitude reduction in leakage, but shielding techniques have never fully measured up to original expectations because of motion-related artifacts, especially ghosting in the phase-encoding direction and battle-zone levels of acoustic noise.
Recovery time is often found to increase quadratically with pulse amplitude, indicating it is related more to motion than to eddy currents. It is in fact arguable that eddy currents per se are no longer a significant problem with typical shielded coils and optimized multi-exponential high-pass compensation that includes first-order cross terms as described by Van Vaals and Bergman, but rather the vibrations produced by the eddy currents in passive shields are the cause of residual image artifacts, as the time constants of the high-order eddy currents in passive shields are generally much less than the mechanical vibration time constants. Kondo et al. in U.S. Pat. No. 5,055,789 disclose a partial solution to the image artifact problem.
The gradient coil design problem is fundamentally limited by the conflicting requirements of fast response and reasonable field linearity (spatially constant gradients) over the sample volume. The major technical problems center around the following: (1) limited available space because of economic considerations, (2) motion-induced artifacts arising from the finite stiffness and mass of the coil support structure, (3) practicable coil winding (or etching) techniques, (4) acoustic noise abatement, and (5) heat dissipation.
The conflicting technical requirements may be partially addressed by means of local planar gradient coils with highly non-linear response, as disclosed by Roemer, U.S. Pat. No. 4,926,125. By adding distortion correction algorithms to the image processing, it is possible to utilize gradients with .+-.40% to .+-.60% non-linearity on one axis in applications where high spatial resolution is required only over a small portion of the image.
The following parameters generally need to be specified for gradient coil systems: gradient coefficient .alpha. (T/Am) (sometimes called gradient efficiency in the prior art), imaging ellipsoid radius r.sub.i (m) and axial length h.sub.i for a specified linearity, inductance L (H), resistance R.sub.E (.OMEGA.), maximum continuous power dissipation P (W), maximum pulse current I.sub.P (A) in a specified B.sub.0, recovery time T.sub.D (s) for a specified pulse, and acoustic noise for a specified pulse sequence in a specified field.
For the fastest imaging techniques, Echo Planar Imaging (EPI) and related techniques, the most important parameters are acoustic noise, recovery time, and gradient power. EPI can produce complete 2-dimensional images in 30 ms and repeat the process several times per second, compared to minimum imaging times of several minutes for conventional spin-echo techniques. In addition to the enormous prospects for increased patient throughput in MRI, EPI allows realtime monitoring of heart valve function and even realtime analysis of brain response to visual and auditory stimuli.
Although EPI was first described 15 years ago, it has seldom been used because prior art gradient coils (a) may require megawatts of gradient driver power on the frequency-encoding axis, (b) generate sound pressure levels that are painful and damaging to the patient's hearing, (c) produce motion-related artifacts that cannot be fully removed even with the most sophisticated image post-processing, and (d) require high power audio amplifiers costing up to several million dollars. A recent experimental demonstration at 0.5 T required nearly half a megawatt (at 10% duty cycle) at one kHz, and others have proposed the use of 2 MW at 5 kHz, 1.5 T, and 50% duty cycle for slice-interleaved techniques. The above problems may be partially addressed using a tuned transverse gradient with sinusoidal (monochromatic) current; but the conventional gradient coil has very low electrical Q; and there are penalties in SNR (signal to noise ratio) and heat dissipation. Also, computational analysis becomes more complex, but that objection is trivial.
While the Maxwell z-gradient is considerably more efficient than the Golay transverse gradient, the frequency-encoding gradient must be in the plane of the image, which often must be transverse for medical reasons. Hence, order-of-magnitude improvements are needed in transverse gradients.
The image artifact problem can begin to be appreciated by noting that while the frequency-encoding gradient may be driven with a 500 kW trapezoidal wave form, the phase-encoding gradient is being driven with short "blips" of several kilowatts at very low duty cycle, and the slice-selection axis is nulled. It is quite easy for non-linear, vibration-dependent couplings between the frequency-encoding axis and the other axes to destroy the required degree of orthogonality between the axes and produce phase-related artifacts. Moreover, cylindrical asymmetries in rf and gradient shields can make the orthogonality frequency and amplitude dependent.
The availability of better image processing and distortion correction techniques suggests that the linearity standard be increased to .+-.20%, compared to the more typical .+-.10% value for prior art whole-body systems. (Linearity in prior art MR microscopy is typically .+-.4% or better because the rf coils require a relatively large exterior dead space, which necessarily makes gradient linearity very good over the small sample region.) Increasing the non-linearity allowance from .+-.10% to .+-.20% increases the imaging volume by typically 50%. It is still important that the field be monotonic, but the method of Schenck et al. in U.S. Pat. No. 4,646,024 results in relatively poor switching efficiency, intolerable acoustic noise, and unmanageable motion-related artifacts.
Designing for large gradient non-linearity with very fast switching capability places increased (though inconsequential) computational demands on the image processing and may result in some increased variation in SNR over the final image. However, the enormous bandwidth (several MHz) of high-resolution EPI (and other more advanced techniques) can reduce the imaging time by two or three orders of magnitude without placing unrealistic demands on modern computers since computational power per cost has increased at the rate of 40% per year for the past seven years and that rate is expected to continue for several more years.
Magnetic energy storage estimates can be enlightening. Assume gradients of 1 T/m over an imaging sphere of 14-mm radius (.+-.20% linearity) for a typical solids microscopy application using a transverse gradient coil of 45-mm diameter. We might then expect maximum gradient fields of about 0.02 T (50% more than the sample's maximum) over a volume of perhaps 60 ml (6 times the sample volume); hence, 0.01 J. Switching this field in 100 .mu.s would require 100 W, assuming relatively low resistive loss, which can easily be achieved. In practice, using conventional shielded gradient coils, the inductive energy (I.sup.2 L/2) is larger than suggested by simple energy estimates as above by a factor of twenty to one hundred.
While most of the wasted magnetic energy in Golay coils is external to the patient in MRI, the unusable magnetic energy (the integral of the rms value of B.sub.X +B.sub.Y) over the patient may be an order of magnitude larger than the usable field (the integral of the rms value of .delta.B.sub.Z /.delta.x or .delta.B.sub.Z /.delta.y over the image volume). It is the switching of this enormous non-gradient field from the Golay geometry that causes the sensory stimuli in patients during EPI experiments and limits clinical applications. It is also this non-gradient field that is responsible for virtually all of the eddy currents and vibrations induced in the rf coils, as the desired gradient field is axial and its dipole moment is zero.
Conventional transverse gradient coils have always been designed from the deeply ingrained perspective that a single large coil is more efficient and less costly than a collection of smaller coils. This notion may be true most of the time, but not when it comes to complex field geometries. Maxwell's laws make it impossible to design coil systems that generate single field gradients (they must come at least in pairs) but it is not necessary to have large orthogonal field components.
Some prior gradient coil designs have also suffered under the false notion that there is an inherent advantage with very low inductance coils. Higher inductance (more turns) requires higher voltage, but not higher power (VA) for the same switching time. In fact, reducing inductance below 100 .mu.H is detrimental as lead inductance and transmission line problems then become significant. Coil orthogonality (for isolation) and net force cancellation both dictate that integral numbers of turns be used in all coil sets and coil subsets. Hence, the accuracy of the shielding is limited from this quantization. The more turns, the more precisely the gradients can be shielded. Optimum number of turns is thus determined largely by the VA characteristics and economics of available power devices, magnetic shielding accuracy requirements, and standard wire insulation practice, making 250 V to 800 V (peak differential voltage for a balanced line) at 10 A to 100 A best for large systems. Optimum inductance is typically 0.2 to 1 mH.